In traditional communication networks, information is delivered as a sequence of packets from source to destination by routing through intermediate nodes which only store and forward those packets. Recent research shows that routing alone is not sufficient to achieve the maximum information transmission rate across a communication network [1]. Network coding is a currently researched topic in information theory that allows the nodes to generate output data by encoding their received data. Thus, nodes may mix the input packets together and send them out as fewer packets. Potential throughput benefit is the initial motivation of the research in network coding. Group communications refers to many-to-many communication sessions where multiple sources multicast independent data to the same group of receivers. Researchers always treat group communications as a simple problem by adding a super source which is connected to all the sources with unbounded capacity links. However, it cannot control the fairness between different sources in this method. Additionally, the method may be incorrect in some scenarios. In this research, we will present an example to illustrate that and analyze the reason for that. The maximum multicast throughput problem using routing only is NP-complete. Wu et al. introduced a greedy tree-packing algorithm based on Prim's algorithm as an alternate sub-optimal solution [2] . This algorithm is modified in this work for group communications problem with routing in undirected networks. The throughput benefit for network coding has been shown in directed networks. However, in undirected networks, researchers have only investigated the multiple unicast sessions problem and one multicast session problem. In most cases, network coding does not seem to yield any throughput benefit [3] [4]. Li et al. introduced a c-flow algorithm using linear programming to find the maximum throughput for one multicast session using network coding [3] . We adapted this algorithm for group communications with network coding in undirected networks to overcome the disadvantage of the traditional method. Both algorithms were simulated using MATLAB and their results were compared. Further, it is demonstrated that network coding does not have constant throughput benefit in undirected networks.